Micromechanical alternating and direct voltage reference apparatus

ABSTRACT

An AC/DC voltage reference system has at least one micromechanically fabricated electrode pair having first and second electrodes facing each other so that the electrodes are disposed at a distance from each other, whereby at least one of the electrodes is movable against a spring force. An AC signal is applied over the electrodes to establish an electrostatic force at a frequency substantially higher than the effective mechanical resonant frequency of the movable electrode. The system further includes an apparatus for detecting the AC voltage applied between the electrodes, thus forming an AC voltage reference.

This application is the national phase under 35 U.S.C. §371 of PCTInternational Application No. PCT/FI99/00553 which has an Internationalfiling date of Jun. 22, 1999, which designated the United States ofAmerica.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a micromechanical AC voltage reference system.

The invention also concerns a micromechanical DC voltage referencesystem.

The invention further concerns an AC/DC converter based on an identicalmechanical structure.

Possibilities of linking electrical quantities to mechanical quantitiesby means of a linear capacitive voltage transducer are contemplated,e.g., in a reference publication “F. Cabiati, “Linking Electrical WithMechanical Quantities Through Electro-Mechanical Resonance,” inConference Digest of CPEM96, pp. 610-611, 1996”. These investigationshave been performed into large electromechanical structures subject tomechanical instability factors and requiring a high bias voltage foroperation.

It is a primary application of an AC/DC converter to measure the RMSvalue of an AC signal using a known DC signal as the reference. The mostaccurate state-of-the-art AC/DC converters are electrothermic transferstandards based on the comparison of ohmic heating caused by the appliedAC and DC signals, respectively. One disadvantage of electrothermicconverters is that they impose a heavy load on the signal sourceconnected to their input.

A problem hampering fully electronic AC/DC converters is theirrelatively low maximum operating frequency and the resulting degradationof accuracy.

AC/DC converters may also be realized using micromechanical electrodestructures operating based on an electrostatic force. The use of asilicon micromechanical capacitive electrode structure in the RMSamplitude measurement of an AC voltage signal is discussed in referencepublication by “B. P. van Drieënhuizen and R. F. Wolffenbuttel, entitled“Integrated Micromachined Electrostatic True RMS-to-DC Converter,” inIEEE Transactions on Instrumentation and Measurement, Vol. 44, No. 2,pp. 370-373, 1995”. The publication describes a bridge structure madefrom polycrystalline silicon by surface micromechanical techniques. Thestructure includes an electrode pair in which one electrode iselastically suspended. An AC voltage applied between the electrodescauses a change in the interelectrode capacitance, the magnitude ofwhich is measured to determine the RMS value of the applied AC voltage.According to this publication, the conversion of the measuredcapacitance into the respective AC RMS voltage was made using anelectronic circuit. Hence, the accuracy of the AC RMS voltagemeasurement is dependent not only on the qualities of themicromechanical structure, but also on those of the above-mentionedelectronic circuit used.

SUMMARY OF THE INVENTION

It is an object of the present invention to overcome the disadvantagesof the above-described prior art techniques and to provide an entirelynovel type of micromechanical AC and DC voltage reference system.

Furthermore, the invention disclosed herein is free from theshortcomings of the above-described micromechanically constructed AC/DCconverter based on the measurement of an electrostatic force.

The goal of the invention is achieved by virtue of a system based on amicromechanical structure comprising at least one electrode pair thatfurther comprises a first electrode and a second electrode disposed at adistance from each other so as to make at least one of said electrodesmovable against a spring force, said system further including means forapplying an AC signal over said electrodes for establishing anelectrostatic force advantageously at a frequency which is substantiallyhigher than the effective mechanical resonant frequency of the movableelectrode and said system further including means for detecting the ACvoltage acting over the electrodes thus creating the AC voltagereference. In an AC/DC converter based on a preferred embodiment of thebridge structure according to the invention, the electrostatic forcescreated by the AC signal and the DC signal are compared directly witheach other using an embodiment of the micromechanical electrodestructure. The electrical circuit measuring the capacitive voltagedivision ratio senses the force balance.

More specifically, the AC voltage standard according to the presentinvention is a system that comprises at least one micromechanicallyfabricated electrode pair. The pair includes a first electrode and asecond electrode adapted to face each other so that the electrodes aredisposed at a distance from each other, so that at least one of theelectrodes is movable against a spring force. Means are provided forapplying an AC signal over the electrodes for establishing anelectrostatic force advantageously at a frequency substantially higherthan the effective mechanical resonant frequency of the movableelectrode. The system also includes an apparatus for detecting the ACvoltage applied between said electrodes, thus forming an AC voltagereference.

Furthermore, the DC voltage standard according to the present inventioncomprises at least one micromechanically fabricated electrode pair. Theelectrode pair includes first and second electrodes facing each other sothat the electrodes are disposed at a distance from each other, and atleast one of the electrodes is movable against a spring force. Means areprovided for applying an electrical charge between the electrodes inorder to deviate the electrodes from their mutual equilibrium position,together with means for detecting the DC voltage applied between theelectrodes, thus forming an DC voltage reference.

Still further, the AC/DC voltage transfer standard system, that is, anAC/DC converter, according to the present invention, comprises at leasttwo micromechanically fabricated electrode pairs disposed at a distancefrom each other so that at least one of the electrodes is movableagainst a spring force. Means are provided for feeding a DC signal onone electrode of the first electrode pair. Also included are means forfeeding an AC signal on one electrode of the second electrode pair, aswell as means for detecting the position of the movable electrode or,alternatively, the force required to maintain the position of theelectrode, to compare the RMS values of the applied AC and DC voltages.

The invention offers significant benefits.

Voltage standards according to the invention based on the advantageousmechanical and geometrical properties of monocrystalline silicon canexhibit an extremely high stability. Also the production costs of suchvoltage standards can be brought to a very reasonable level.

As the electronic circuit of an AC/DC converter according to a preferredembodiment of the invention essentially acts as a zero-positionindicator, the problems occurring from, e.g., nonlinearities ofelectronics are avoided and thus an entirely novel type of AD/DCconverter is accomplished.

DESCRIPTION OF THE DRAWINGS

In the following, the invention will be examined in greater detail withthe help of exemplifying embodiments illustrated in the appendeddrawings, in which

FIG. 1 shows a block diagram of an AC voltage standard according to theinvention;

FIG. 2 shows a plot of the electrode voltage dependence on the capacitorcharge as measured using the equipment illustrated in FIG. 1;

FIG. 3 shows a block diagram of a DC voltage standard according to theinvention;

FIG. 4 shows a longitudinally sectional top view of a mechanicalembodiment according to the invention, suitable for use as a DC voltagestandard and an AC/DC converter;

FIG. 5 shows a cross-sectional view of an alternative embodimentaccording to the invention;

FIG. 6 shows the embodiment illustrated in FIG. 5, here sectioned in theplane of the. beam element 22;

FIG. 7 shows a circuit configuration suitable for use in conjunctionwith the embodiment illustrated in FIG. 4;

FIG. 8 shows a circuit configuration suitable for use in conjunctionwith the systems illustrated in FIGS. 4 and 5 for resetting thequiescent operating frequency and controlling the rest position of thesystem; FIG. 9 shows schematically an alternative circuit configurationsuitable for implementing an AC voltage standard; and

FIG. 10 is a plot elucidating the function of the circuit configurationshown in FIG. 9.

DESCRIPTION OF THE INVENTION

Accordingly, the invention relates to micromechanical AC and DCstandards suited for use in miniature and cost-efficient constructionsof precision electronics. The text of the present application alsodiscusses the basic operating principle of this type of AC and DCstandards as well as the preliminary tests performed on the novelstandards. High-precision voltage standards are utilized in measurementequipment, for instance.

The text also describes an embodiment of an AC/DC converter based on thesame mechanical basic construction.

Improved fabrication methods of silicon components (including the use ofSilicon-on-Insulator, SOI, substrates) facilitate the manufacture ofminiature structures from monocrystalline silicon. Such structures aremechanically extremely stable. Miniature voltage standards of highstability and cost-efficient construction can be made by combining theelectrical stability of standards with the mechanical stability of SOIstructures. To attain this goal, the text of this application disclosestwo basic concepts.

The AC voltage standard according to the invention is based on a planarcapacitor having at least one of its electrodes suspended in an elasticmanner on the surrounding structures this making said electrode movablein regard to the other structures. In an ideal moving-plate capacitor(MPC) having planar electrodes, the capacitance is C=εA/(d−x), where xis the deviation of the moving electrode (ME) from its static positionunder electrostatic forces and (d−x) is the interelectrode distance. Thedisplacement of the moving electrode ME is determined by the equation ofa forced harmonic oscillator: $\begin{matrix}{{{{m\quad \frac{^{2}x}{t^{2}}} + {\lambda \quad \frac{x}{t}} + {kx}} = F_{el}},} & (1)\end{matrix}$

written using the symbols according to the standard convention ofphysics. If a sinusoidal current i=î₀ sin ωt is passed via a capacitor,the charge of the capacitor is q=(î₀/ω)(1−cos ωt)+q₀, where q₀ is thecapacitor charge at instant t=0. The electrostatic force between theplanar electrodes is F_(el)=q²/(2εA). Then, the exact steady-statesolution of Eq. (1) is $\begin{matrix}{{x = {\frac{q\quad \omega^{2}}{2\quad ɛ\quad {Ak}}\lbrack {1 + {{A( {2\omega} )}\cos \quad 2\quad \omega \quad t} + {{B( {2\quad \omega} )}\sin \quad 2\quad \omega \quad t}} \rbrack}},} & (2)\end{matrix}$

where${{A^{- 1}(\omega)} = {\frac{( {\delta^{2} - 1} )^{2} - {( {{\lambda/m}\quad \omega_{0}} )^{2}\delta^{2}}}{\delta^{2} - 1} \approx \delta^{2}}},{{B^{- 1}(\omega)} = {{{{Q_{m}( {1 - \delta^{2}} )}^{2}/\delta} + {Q_{m}^{- 1}\delta}} \approx {Q_{m}\delta^{3}}}},\quad {and}$${q_{\omega} = {{{\hat{i}}_{0}/\sqrt{2\quad}}\omega}},\quad {\omega_{0} = \sqrt{k/m}},\quad {Q_{m} = {{{\sqrt{km}/\lambda}\quad {and}{\quad \quad}\delta} = {\omega/{\omega_{0}.}}}}$

Herein, an assumption has been made that

q ₀=−{square root over (2)}q _(ω),

whereby the average electrostatic energy stored in the capacitor isminimized so that the DC voltage component over the capacitor is zero.Herein, the terms containing A(ω) and B(ω) can be neglected providedthat the frequency ω of the alternating control current is substantiallyhigh in regard to the mechanical resonant frequency ω₀ of the capacitor,in other words meaning that δ >>1, a condition called later in the textas a high operating frequency assumption. Parallel to the term referringto the pure mechanical resonant frequency, the same variable may alsoappropriately called the effective mechanical resonant frequency whenthere is a need to indicate that the effect of a possible electricalcontrol (e.g., through DC biasing) on the inherent mechanical resonantfrequency has been taken into account.

The amplitude of the AC voltage over the capacitor is $\begin{matrix}{{{\hat{u}}_{\omega} = {\frac{\sqrt{2}q_{\omega}}{C_{0}}\lbrack {1 - \quad {\frac{4}{27}( \frac{q_{\omega}}{C_{0}u_{pi}} )^{2}}} \rbrack}},} & (3)\end{matrix}$

where C₀=εA/d and $u_{pi}^{2} = {\frac{8}{27}{{kd}^{2}/{C_{0}.}}}$

From Eq. (3) can be seen that the amplitude û_(ω) has a maximum valueû_(max)={square root over (2)}_(pi) when$q_{\omega} = {q_{\max} = {{\pm \quad \frac{3}{2}}C_{0}{u_{pi}.}}}$

This characteristic amplitude value û_(max) can be used as a referencevoltage, because a change in the value of î₀ does not have afirst-degree effect on the value of û_(max). If the amplitude inaccuracyof the current that causes said voltage is Δî₀, the relative inaccuracyof said voltage at its maximum value is${\Delta {{\hat{u}}_{\omega}/{\hat{u}}_{\omega}}} \approx {\frac{3}{2}{( {\Delta {{\hat{i}}_{0}/{\hat{i}}_{0}}} )^{2}.}}$

To verify these relationships, also the effect of the stray capacitanceand the spectral purity of the current source output signal waveformwere examined by the inventors using numerical simulations. Inpreliminary tests, measurements were performed using an AC currentcontrol system illustrated in FIG. 1, wherein the planar capacitor 1 wasfabricated using surface micromechanical techniques. The testedcapacitive sensor comprises a movable electrode 7 and a stationaryelectrode 8. An operational amplifier 2 was used as a voltage-to-currentconverter. The AC current to the capacitor 1 was supplied by a signalgenerator 3, whose output voltage was converted by a current-to-voltageconverter 2 into an AC current control signal. In the actual circuitconfiguration, the AC current control of the sensor 1 was implemented byplacing the sensor 1 on the feedback path of the current-to-voltageconverter 2. The exemplifying component values in the circuitconfiguration of FIG. 1 were: R_(f)=22 Mohm, R_(i)=10 kohm, R₀=100 ohmand C_(i)=100 nF. The current passing through the capacitor 1 wasestimated as î₀={circumflex over (V)}_(in)/R₁ and the voltage over thecapacitor 1 as ({circumflex over (V)}_(out)−{circumflex over (V)}_(in)).The measurements were performed by measuring the values of {circumflexover (V)}_(in) and {circumflex over (V)}_(out) when {circumflex over(V)}_(in) was increased slowly. In the measurement layout, the digitalvoltage meters DVM1 and DVM2 and the signal generator are connected inparallel with the computer PC on an instrumentation bus (GPIP BUS). Whenthe sensor 1 is driven into its most stable operating range by means ofthe signal generator 3, an extremely stable output voltage is attainedsuitable for use as a voltage reference signal V_(out), a condition thatcan be verified by means of the digital voltage meter DVM1.

In curve 5 of FIG. 2 is shown a plot of the voltage measured over thecapacitor 1 of the circuit of FIG. 1 as a function of q_(ω).Furthermore, in curve 6 of FIG. 2 is shown with a dashed line thevoltage theoretically computed from Eq. (3). Curve 5 representing themeasured voltage exhibits a sudden dip at q_(ω)≈130 pC (RMS), caused bythe tendency of the planar capacitor electrodes 7 and 8 to pull in untilthey hit the spacers made in the interelectrode space. This pull-ineffect is a result of the sensor stray capacitance and the nonzerocondition of the DC voltage acting over the capacitor. In order to copewith these anomalies resulting from the nonideal behaviour of thecapacitor, the horizontal and vertical axes of the theoreticallycomputed curve are scaled with correction factors having values of 0.95and 0.80, respectively. Hence, an accurate voltage standard can beaccomplished by driving the silicon micromechanical construction tooperate within the flat peak of the characteristic curve plotted in FIG.2, whereby a change in the alternating control current causes a minimalchange in the voltage output used as a voltage standard.

In a static situation, the force imposed by the DC charge on the movableelectrode ME is${F_{el} = {{\frac{1}{2}ɛ\quad {{Au}^{2}/( {d - x} )^{2}}} = {{q^{2}/2}ɛ\quad A}}},$

whereby it can be computed from the equation of an equilibrium situation$\begin{matrix}{u^{2} = {\frac{2k}{C_{0}}{{dx}( {1 - {x/d}} )}^{2}}} & (4)\end{matrix}$

that the DC voltage u over the capacitor reaches a maximum valueu=u_(pi) when x=d/3.

In FIG. 3 is shown the block diagram of a DC voltage standard based onthe above described concept. The mechanical structure of the standardcan be implemented as shown in FIGS. 4, 5 and 6. The structure showntherein may comprise, e.g., a beam 14 connected in an elastic manner byits center to the surrounding structure so as to form a micromechanical“balance” 13. To both ends of the balance 13 are symmetrically formedfour capacitors C₁, C₂, C₃ and C₄. The capacitors C₁ and C₂ are fed by avoltage source 10 so that the voltage over capacitor C₁ can be adjustedby resistive voltage division R₁/R₂ and the voltage to be applied over abalancing capacitor C₂ is respectively passed via an inverter 11 to theelectrode of said balancing capacitor C₂. A feedback circuit PI controlsthe DC charge of capacitor C₃ such that sets the capacitance ratio ofthe capacitors C₁ and C₂ equal to the division ratio of the resistivedivider (R₁+R₂)/R₂. The input of the PI circuit is fed by a mixer 12whose one input in turn senses the amplitude of the signal measured by acharge-sensitive amplifier CA from the balance beam 14 at the frequencyof the signal delivered by the voltage source 10. Provided thatC₁/C₂=C₄/C₃, in the equilibrium situation x=rd=d/(1+2R₂/R₁). When theresistance of R₁ is increased from zero to infinite, the beam deflectionchanges from zero to d, and when R₁=R₂, the voltage u reaches a maximumvalue. At this operating point, the relative change of the bridge outputvoltage is substantially smaller than a relative change in the ratio ofcapacitances or in the ratio of the resistances. Herein, it must benoted that the forces imposed by the sensing currents on the capacitorsC₁, C₂ cancel each other when the bridge is in equilibrium. In thismanner, the stable mechanical structure allows the value of the bridgeoutput voltage u to be used as a DC voltage reference. Obviously, thebridge output voltage u needs to be detected by a suitable circuitry notshown in the diagram.

On the same principle, it is further possible to construct DC and ACvoltage standards based on a mechanical resonant frequency shiftoccurring in micromechanical oscillators having a high Q factor.

In a practicable embodiment, such standards may additionally need asupplementary circuit arranged to perform a continuous search for themaximum voltage peak of the operating curve.

The embodiment according to the invention may also be used as anintegrated circuit, whereby external means for output voltage detectionare redundant.

In FIGS. 4, 5 and 6 are shown the structure and electrical circuitconfiguration of an AC/DC converter embodiment.

Using the micromechanical constructions illustrated in FIGS. 4, 5 and 6,both an AC/DC converter and a DC voltage standard can be realized. InFIGS. 7 and 8 is shown the electrical circuit configuration of an AC/DCconverter that is basically similar to the above-described DC voltagestandard.

As shown in the diagrams, an AC/DC converter compares the electrostaticforces imposed by both the DC and the AC voltages, and thereby, theeffective values of both voltages to each other. The DC voltage is takento electrode 34 and the AC voltage to electrode 35. The electrodes 30and 31 are used for sensing the position of the elastically suspendedbalance beam 22. If the electrostatic forces imposed by the appliedvoltages are not equal, the beam 22 moves (cf. FIG. 4) or,alternatively, rotates (cf. FIGS. 5 and 6) by a distance that isproportional to the difference between the imposed forces. In theillustrated embodiment, a force-feedback arrangement is used in whichthe beam 22 is equilibrated and the difference of the opposing forces issensed from the feedback force required to maintain the equilibrium. Theelectrical ground potential plane is denoted by reference numeral 25.

The micromechanical structure shown in FIG. 4 can be fabricated, e.g.,on a SOI substrate by material etch-away so that a structure 22 isformed capable of elastically moving in the plane of the substrate, saidmovable structure having four comb electrodes made thereon for thepurpose of position control and sensing. The ends of the movablestructure are mechanically anchored on suspension members 32. In FIG. 4,the movable structure 22 fabricated free from its substrate and thesuspension member 32 of the structure are denoted by a different patternvs. solid color. The electrode structure is made such that theelectrostatic force acting, e.g., between the electrode 30 and the beam22 tends to move the beam in a direction opposite to that imposed by theelectrostatic force acting between the electrode 31 and the beam 22.Similarly, electrodes 34 and 35 effect forces opposing each other.

Another embodiment of an equivalent micromechanical structure is shownin FIGS. 5 and 6. Herein, the electrode movement is not linear buttorsional. The movable beam is mechanically anchored on a suspensionmember structure 32. Electrodes 30, 31, 34 and 35 are patterned on aninsulating substrate such as glass.

Obviously, the geometry and layout of the electrodes may be varied fromthose shown in the exemplifying embodiments. An essential property ofthe construction is that the forces imposed by the AC and DC electrodeson the movable structure are arranged to act substantially opposite toeach other.

In FIG. 7 are shown the electrical connections of an AC/DC convertermade to the electrodes 34 and 35 forming the force balance construction.When the outputs of a two-position quad switch 36 are toggled to theright-side quad group of conductors, the DC voltage source 17 isswitched to electrode 34 and the AC voltage source 18 to electrode 35.The DC voltage is sensed on conductor 19 and, respectively, the ACvoltage on conductor 20. Using separate feed and sense lines, the effectof conductor resistance can be eliminated. Next, when the quad switch 36is toggled to the left-side quad group of conductors, the roles of theelectrodes 34 and 35 are reversed. By toggling the position of the quadswitch 36 in this manner, the effect of parameter drift in theelectronic circuitry of the measurement system and in the mechanicalstructure of the converter can be reduced in the AC/DC transfercomparison. The lower silicon plane 16 of the SOI substrate 15 isadvantageously taken to the electrical ground potential. The electricalground potential areas of the surface layer formed on the SOI substrateare denoted by reference numeral 25. Using a suitable design of theground-potential layer elements, the mutual capacitive coupling betweenthe electrodes 30, 31, 34 and 35 may be effectively reduced in themanner shown in FIGS. 4, 5 and 6.

In FIG. 8 is shown the electronics circuitry for beam position sensing.The position of the center beam 22 is advantageously sensed using ameasurement frequency in the range of 10-100 MHz applied on the beam byinductive means so as to pass charges on the capacitive elementsparticipating in the measurement. The current passed via the beam 22 tothe ground potential is detected. The current via the beam is the sum ofthe currents passing via the capacitive elements acting as themeasurement electrodes 30 and 3 1. The current via the beam 22 to theground potential is zeroed by altering the DC potential applied on themeasurement electrode 31, whereby the beam position is changed so as toalter the currents passing via the capacitive elements 30 and 31.Differential amplifier 24 senses the difference between the DCpotentials applied on the capacitive elements 30 and 31, thus indicatingthe AC/DC transfer balance situation. The effect of a possible offsetvoltage is eliminated by measuring the output voltage in a situationwhen all the AC and DC voltages to be measured are set to zero.

This type of an AC/DC converter operates at AC voltage frequenciessubstantially higher than the mechanical resonant frequency of the beamwhich in typical micro-mechanical structures is in the order of a fewkHz. The operating range of an AC/DC converter can be increased bylowering the resonant frequency of mechanically resonating components byvirtue of an electrical control. This can be accomplished by applying anequal DC voltage U_(b) to the electrodes adapted symmetrically to bothsides of the beam 22. Then, the electrically controlled mechanicalresonant frequency ω_(me) is ω_(me)/ω_(m)=(1−αU^(b) ²/U_(pi) ²)^(½) and,at least theoretically, its value can be brought as low as to zero Hz.The constant α is in the order of one. For a planar capacitor, α=16/27.

To lower the mechanical resonant frequency, the circuit shown in FIG. 8can be operated so that a bias voltage U_(b) is applied to onemeasurement electrode 30. Then, the control loop of the circuit bringsthe DC potential of the other electrode 31 to the same level, wherebythe mechanical resonant frequency of the beam is lowered. The resonantfrequency also remains low also in a situation, in which the differencein the forces imposed by the AC and the DC voltages, as measured by theelectrodes 34 and 35, causes a differential force that tends to move thebeam, whereby said force is compensated for by controlling the DCpotentials applied on the measurement electrodes 30 and 31 to levelsdifferent from each other.

In the embodiment shown in FIG. 8, it is essential to set |U_(b)|>0, inorder to allow the force feedback to function in a situation in whichthe electrostatic force imposed by the charge of the electrode 34 to begreater than the force imposed by the charge of the electrode 35 andvice versa.

If the effective electrode areas of the capacitive elements or theirpermittivities differ from each other, the measurement currents impose adeflecting force on the beam 22. The situation can be balanced byadjusting the currents passed to the electrodes slightly different fromeach other. This offset can be accomplished by means of, e.g., adjustingthe resistance of resistor 37 about that of resistor 38.

The beam 22 should be operated as close as possible to the electricalground potential. Herein, problems may occur due to the seriesresistance of the mechanical suspension of the beam. A portion of thepotential drop in the AC voltage applied to terminal 18 is lost asvoltage loss over a resistance, whereby the electrostatic beam-deviatingforce imposed via the AC electrodes is reduced. The relative loss of thedeviating force is proportional to the square of the ratio of the seriesresistance to the capacitive reactance. The series resistance of thebeam suspension can be minimized by using a silicon material ofmaximally high conductivity and, when required, metallization of thebeam suspension elements. The remaining portion of resistive loss in theAC voltage feed path can be compensated for by applying on the beam asmall corrective voltage at 180° phase shift in regard to the AC voltagebeing measured.

The above-described method induces a small AC voltage component on thepotential of the DC electrode, possibly also a small component of thehigh-frequency sensing signal used for detecting the position of thebridge. When both an AC and a DC voltage is applied between twoelectrodes, the time-averaged force generated therefrom can be writtenas$F = {{\frac{ɛ\quad A}{2l^{2}}\overset{\_}{( {U_{dc} + {{\hat{U}}_{ac}\sin \quad \omega \quad t}} )^{2}}} = {\frac{ɛ\quad A}{2l^{2}}( {U_{dc}^{2} + {{\hat{U}}_{ac}^{2}/2}} )}}$

If the goal is to keep the force inaccuracy below 1 ppm, an AC voltagesignal of about 10⁻³ U_(dc) maximum can be superimposed on the DCvoltage signal. As can be seen herefrom, the mixing of uncorrelatedsignals in this type of AC/DC converter is not a particularly seriousproblem. Also the electrostatic force generated by the distortioncomponents of the AC source signal is summed on the force imposed by thefundamental frequency signal in a squared RMS voltage ratio of saidcomponents to the basic signal.

In FIG. 9 is shown an alternative embodiment of an AC voltage standard.Herein, a series-connected inductor L₄₀ forms an electrical LC resonatorwith a micromechanical capacitor C₄₁. In the diagram, resistor R₄₂represents the combination of electrical losses with possible lumpresistances and output impedance of the oscillator delivering the ACcontrol voltage V_(2in). Parasitic capacitances acting in parallel withthe micromechanical capacitor C₄₁ are denoted by a lump capacitanceC_(stray)=C₄₃. The AC voltage V_(2out) providing the accurate ACreference is detected by measuring the AC voltage acting over capacitorC₄₁. The circuit shown in the diagram uses a voltage-follower amplifier44 as a buffer whose output provides the desired signal V_(2out).

Using the above-described circuit, the micromechanically fabricatedmovable planar electrode of capacitor C₄₁ can be driven into a positionin which the RMS value of the AC voltage applied over the capacitorattains the value u_(pi) defined by Eq. (3). The basic idea herein is toselect the frequency f=ω/2π of the AC control voltage so that when thedeviation of the planar capacitor electrode is equal to the value thatproduces the voltage maximum, also the capacitance is driven to a valuemaking the LC resonator to be in its electrical resonance or at leastsubstantially close thereto. Then, small variations in the level of thecontrol voltage have a minimal effect on the level of the AC voltageapplied over the capacitor.

Provided that the earlier mentioned high-frequency assumption is valid,the RMS value of the voltage applied over the electrodes is

û _(ω) =V2_(inRMS)/{square root over (ω² R ² C _(t) ²+(ω² LC _(t)−1)²)},where C _(t) =C ₄₁ +C ₄₃ , C ₄₁ =C ₀/(1−x/d) and C ₀ =εA/d. Then, theelectrostatic force is

$\frac{F_{el}}{kd} = {\frac{4{V2}_{inRMS}^{2}C_{41}^{2}}{27u_{pi}^{2}C_{0}^{2}} \times {\frac{1}{{\omega^{2}R^{2}C_{t}^{2}} + ( {{\omega^{2}{LC}_{t}} - 1} )^{2}}.}}$

 The electrical resonant frequency is ω_(e) ={square root over(C₀/C_(t))}ω ₀, where ω₀ ={square root over (1/LC ₀)}. The qualityfactor Q at resonance is Q _(e) =Q ₀ {square root over (C₀/C_(t))},where Q ₀ ={square root over (L/R²C₀)}.

The benefits of the novel circuit can be appreciated from acomputational example. In FIG. 10 is shown the amplitude V_(2out) of theAC voltage measured over the planar electrodes as a function of thecontrol voltage V_(2in). Both of the plotted voltage curves are scaledrelative to the pull-in voltage. Additionally, the voltage scale of thehorizontal axis is multiplied by the electrical quality factor Q₀ of thecircuit. The control voltage is applied over the resonant tuning circuitunder conditions in which ω/ω₀ ={square root over (2/3)}, Q ₀={squareroot over (L/C₀)}/R=100 and C_(stray)=C₄₃=0. In the example, the controlvoltage frequency ω is selected such that when the ideal moving-platecapacitor (MPC) is driven into position x=d/3, the resonant frequency ofthe tuning circuit formed by the capacitance and the inductance is justequal to the control frequency, that is, ω/ω₀=⅔.

In the plot of FIG. 10, the curve drawn by a solid line represents theratio V_(2outRMS)/u_(pi) and the curve drawn by a dashed line is theratio x/d. The curves are plotted by solving Eq. (1) of the dynamicmovement using numerical computations, starting from a large value(larger than ≈1.38), of Q₀V_(2inRMS)/u_(pi), whereby the solution isstill on the broad top of the curve, that is, x≈d/3, and then loweringthe control voltage V_(2inRMS)/u_(pi) slowly toward the zero level.

When the behaviour of the output voltage is examined on an enlargedscale, it can be seen that in the surrounding of pointQ₀V_(2inRMS)/u_(pi)≈1.39 a relative change of about 1% in the controlvoltage close to the quiescent operating point V_(2outRMS)/u_(pi) causesa change of only about 2 ppm (parts per million) in the output voltage.Hence, by selecting the quiescent operating point of the control voltageof the AC voltage standard so that operation within the range of theflat top of the operating curve can be assured, a measurement system isobtained exhibiting a minimal dependence on variations in the controlvoltage level. The dependence of the output voltage on the controlvoltage level is the smaller the closer the operating point is set tothe left edge of the flat top of the operating curve. However, theoperating point must be selected so that variations in the controlvoltage level cannot cause a shift of the operating point from the flattop occurring at point x≈d/3 to the vicinity of the point x≈0.

It is obvious to a person versed in the art that the circuitconfiguration shown in FIG. 9 if biased to operate on the flat top ofits characteristic curve may be used for stabilizing an ac voltage inthe same manner as it serves to provide an accurate ac voltage standard.

What is claimed is:
 1. An AC voltage reference system, comprising: atleast one micromechanically fabricated electrode pair including a firstelectrode and a second electrode adapted to face each other so that theelectrodes are disposed at a distance from each other, whereby at leastone of said electrodes is movable against a spring force, means forapplying an AC signal over said electrodes for establishing anelectrostatic force advantageously at a frequency which is substantiallyhigher than the effective mechanical resonant frequency of the movableelectrode, and an apparatus for detecting the AC voltage applied betweensaid electrodes, thus forming an AC voltage reference.
 2. The systemaccording to claim 1, wherein said electrode structure is made frommonocrystalline silicon.
 3. The system according to claim 1, whereinsaid electrode structure includes two electrode pairs connected to abridge configuration.
 4. The system according to claim 1, wherein atleast one of the electrode pairs is driven by a DC signal and the otherby an AC signal in order to implement an AC/DC converter.
 5. An DCvoltage reference system, comprising: at least one micromechanicallyfabricated electrode pair said electrode pair further including a firstelectrode and a second electrode facing each other so that theelectrodes are disposed at a distance from each other, and at least oneof said electrodes is movable against a spring force, means for applyingan electrical charge between said electrodes in order to deviate saidelectrodes from their mutual equilibrium position, and means fordetecting the DC voltage applied between said electrodes, thus formingan DC voltage reference.
 6. The system according to claim 4 or whereinsaid electrode structure is made from monocrystalline silicon.
 7. Thesystem according to claim 5, wherein said electrode structure isincludes two electrode pairs connected in a bridge configuration.
 8. Thesystem according to claim 6, wherein one of the electrode pairs isdriven by a DC signal and the other by an AC signal to implement anAC/DC converter.
 9. An AC/DC converter, comprising: at least twomicromechanically fabricated electrode pairs, disposed at a distancefrom each other so that at least one of said electrodes is movableagainst a spring force, means for feeding a DC signal on one electrodeof said first electrode pair and means for feeding an AC signal on oneelectrode of said second electrode pair, and means for detecting theposition of said movable electrode or, alternatively, for detecting theforce required to maintain said said position of said electrode, thusaccomplishing the mutual comparison of the RMS values of said applied ACand DC voltages with each other.